Recurrent critical points and typical limit sets of rational maps
نویسندگان
چکیده
منابع مشابه
On Rational Maps with Two Critical Points
This is a preliminary investigation of the geometry and dynamics of rational maps with only two critical points.
متن کاملDense Set of Negative Schwarzian Maps Whose Critical Points Have Minimal Limit Sets
We study C2-structural stability of interval maps with negative Schwarzian. It turns out that for a dense set of maps critical points either have trajectories attracted to attracting periodic orbits or are persistently recurrent. It follows that for any structurally stable unimodal map the ω-limit set of the critical point is minimal.
متن کاملRational Points in Cantor Sets
The Idea for this article was given by a problem in real analysis. We wanted to determine the one-dimensional Lebesgue-measure of the set f(C)9 where C stands for the classical triadic Cantor set and/is the Cantor-function, which is also known as "devil's staircase." We could see immediately that to determine the above measure we needed to know which dyadic rationals were contained in C. We soo...
متن کاملCritical Notice Rational Starting Points
Epistemic justification has been claimed to be a special case of argument by philosophers such as Accordingly for each attempt, epistemic justification is the occasion of the arguer making a case for some conclusion based on other premises, when the audience and the arguer are the same person. The dialectical model of argument is used to inform how it is that a subject could come to justify her...
متن کاملPreperiodic points for families of rational maps
Let X be a smooth curve defined over Q̄, let a, b ∈ P(Q̄) and let fλ(x) ∈ Q̄(x) be an algebraic family of rational maps indexed by all λ ∈ X(C). We study whether there exist infinitely many λ ∈ X(C) such that both a and b are preperiodic for fλ. In particular, we show that if P,Q ∈ Q̄[x] such that deg(P ) 2 + deg(Q), and if a, b ∈ Q̄ such that a is periodic for P (x)/Q(x), but b is not preperiodic f...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1999
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-99-04721-8